Teaching the applications of optimisation in game theory's zero sum and non-zero sum games
AbstractWe apply linear and non-linear programming to find the solutions for Nash equilibriums and Nash arbitration in game theory problems. Linear programming was shown as a viable method for solving mixed strategy zero-sum games. We review this methodology and suggest a class of zero-sum game theory problems that are well suited for linear programming. We applied this theory of linear programming to non-zero sum games. We suggest and apply a separate formulation for a maximising linear programming problem for each player. We move on the Nash arbitration method and remodel this problem as a non-linear optimisation problem. We take the game's payoff matrix and we form a convex polygon. Having found the status quo point (x*, y*), we maximise the product (x-x*)(y-y*) over the convex polygon using KTC non-linear optimisation techniques. The results give additional insights into game theory analysis.
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Bibliographic InfoArticle provided by Inderscience Enterprises Ltd in its journal Int. J. of Data Analysis Techniques and Strategies.
Volume (Year): 2 (2010)
Issue (Month): 3 ()
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Web page: http://www.inderscience.com/browse/index.php?journalID=282
nonlinear optimisation; game theory; linear programming; Nash equilibrium; Nash arbitration; non-zero sum games; zero sum games.;
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